Concept 6 of 9
Mode & Range: The Star and the Spread
Today's big idea
Mode is the value that repeats most, and range is the largest take away the smallest.
A set can have one mode, several modes, or no mode at all.
How it works
👀 What's going on?
Ask a class how many pets they have and one answer comes back more often than any other. That is one useful number. How far apart the biggest and smallest answers sit is another.
💡 Here's the trick
The mode is the value that appears most often. The range is the largest value take away the smallest, and it tells you how spread out the data is. A set can have one mode, several modes, or none at all.
🪄 How to do it
- 1.Look through the values in the picture above and find the one that repeats most.
- 2.Find the largest value and the smallest.
- 3.Subtract the smallest from the largest to get the range.
✍️ Try it
One set of scores is 8, 3, 8, 5, 8, 2 and 9. A set of pencil counts is 2, 4, 4, 5, 2, 4 and 6. Give the mode and the range for each.
In the scores, 8 appears three times, so the mode is 8 and the range is 9 take away 2, which is 7. In the pencils, 4 appears three times, so the mode is 4 and the range is 6 take away 2, which is 4.
⚠️ Watch out
The range is a gap, not one of the values. It usually does not appear anywhere in the list at all, so hunting for it among the numbers will send you wrong.
🌟 Why this matters
Between them these two numbers describe a whole set in one breath. The most common shoe size and how much sizes vary. A usual bus journey and how much it swings either side.
Exam tip: Put the list in order from smallest to largest first, because that hands you the range at the two ends and pushes any repeats together.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Data: {2, 7, 2, 5, 2, 9}. Find the mode.”
- 1
Count each value
7 appears once. 2 appears 3 times. 5 once. 9 once.
- 2
Find the most frequent
2 has the highest count.
- 3
That's the MODE
Mode = the value that appears most often.
- 4
Answer ✓
Mode = 2
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
MODE = the value that appears most often. RANGE = biggest − smallest.
Data Set
Tap the MODE — the value that appears most often.
Each unique value above is a chip. Pick the one that repeats most in the data.
Quick check
✅ VERIFICATION
In the set {4, 7, 4, 9, 4, 2}, what is the RANGE?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Reading the Story
Spot the punchline, biggest, smallest, the difference.